Thursday, July 12, 2012

Fortune Favors the Brave: Eratosthenes and the Circumference of the Earth



One of the most persistent myths is the belief that Christopher Columbus sailed to the New World in order to prove that the earth was round. In fact, learned people had known this for several centuries before he was born. People had observed that the earth’s shadow during a lunar eclipse is always circular. And they knew that the only object that casts a circular shadow from every direction is a sphere.
And the natural next question to be answered was how big that sphere is. Greek scientists proposed many answers based on various conjectures. Remarkably, one of them actually figured it out.


In the 3rd century B.C., Eratosthenes, a native of Alexandria Egypt, realized something as simple as a shadow could be used to solve this problem. He knew that on the summer solstice, the sun was directly overhead at the southern Egyptian city of Syene (modern day Aswan). In Alexandria, at the same time, the sun is at a 1/50th declination from being directly overhead (which could be accurately measured using shadows). 

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Taking just that information, Eratosthenes knew that he could calculate the circumference of the earth as long as he knew how far apart Alexandria and Syene are. Estimating that distance based merely on how long it took him to go from one city to the other on a camel, he arrived at the figure of 5000 stadia. There is some debate about what Eratosthenes’ stadia was equal to. But if we assume that it was the Egyptian stadion, his calculations arrive at 25,000 miles for the circumference of the earth. That is less than a hundred miles off from what scientists today measure as the circumference (24,902). When you consider that we also today know that the earth is not even a perfect sphere (it bulges a bit at the equator), Eratosthenes breakthrough is astounding.
The story of Eratosthenes shows us that the solution to a problem can sometimes be a matter of approaching it from a different angle. In this case, it let a man learn the true size of the world for the first time, all without ever leaving Egypt.

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